Finding such conserved quantities demands to know the underlying dynamics, which is not an easy task in human motion where a same – even simple – action requires sometimes very different motor commands. For instance, consider reaching for a cup of coffee on the breakfast table or in an aircraft subject to turbulences, or drinking while seated or while walking. Planning efficient actions is challenging for the brain. It is therefore natural that the central nervous system relies on constants in this jungle of variability. Previous research demonstrated that some classes of actions result from an optimization process in which movements features are taken into account, such as minimizing jerk [1]}, metabolic cost [2]}, [3]} or maintaining a nearly constant mechanical energy in level walking [4]}. Here we study rhythmic motion in time-changing gravity as a peculiar case of time-dependent dynamical system with bounded motion. The most powerful tools known so far to study such systems are adiabatic invariants [5]}, [6]}, [7]}. They have been applied in a wide range of applications such as plasma physics [8]} and cosmology [9]}. In biomechanics, several studies have showed the invariance of the action variable in time-independent conditions [10]}, [11]}, [12]}, [13]}. In a previous work, we went a step further and proposed to use adiabatic invariants to study the changes in the motion of upper arm rhythmic movements about the elbow at free pace and amplitude in a centrifuge where the perceived gravity's intensity changed stepwise from 1 to 3 \(g\)  and from 3 back to 1 \(g\)  [14]}. The direction of \(\vec{g}\)  was unchanged. It appeared that the behaviour of the adiabatic invariant \(I = \frac{1}{2\pi }\oint _{\Gamma } P\, dQ\)  computed from the latter one-degree-of-freedom motion was compatible with a theoretically predicted linear increase with \(g\)  [15]}.
